Global weak solutions for an incompressible charged fluid with multi-scale couplings: Initial-boundary-value problem

Joseph W. Jerome*, Riccardo Sacco

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

The Cauchy problem for the Poisson-Nernst-Planck/Navier-Stokes model was investigated by the first author in [J.W. Jerome, An analytical approach to charge transport in a moving medium, Transport Theory Statist. Phys. 31 (2002) 333-366], where a local existence-uniqueness theory was demonstrated, based upon Kato's framework for examining evolution equations. In this article, the existence of a global weak solution is proved to hold for the model, in the case of initial-boundary-value problem. Connection of the above analysis to significant applications is addressed, including bio-hybrid devices in neuronal cell monitoring, bio-reactor devices in tissue engineering and microfluidic devices in Lab-On-Chip technology.

Original languageEnglish (US)
Pages (from-to)e2487-e2497
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number12
DOIs
StatePublished - Dec 15 2009

Keywords

  • Initial-boundary problem for hybrid systems
  • Navier-Stokes
  • Poisson-Nernst-Planck
  • Rothe's method
  • Slip boundary condition

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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